Dynamic Programming for Quantum Algorithm Design

Jincheng Zhang

Published Sep 6, 2026• 0 citations

Abstract

The design of efficient quantum algorithms frequently relies on intuitive heuristics and extensive trial-and-error processes. This research proposes a novel dynamic programming (DP) framework to systematically explore the vast space of potential quantum circuits, aiming to optimize both circuit structure and gate sequences based on computational cost and expected fidelity. The framework utilizes a bottom-up approach, building solutions from smaller subproblems, leveraging previously computed results to avoid redundant calculations. This approach contrasts with traditional, often ad-hoc, methods for quantum algorithm design. The core contribution lies in formally applying dynamic programming to this problem, providing a structured methodology for algorithm development that can potentially reduce the reliance on guesswork and accelerate the discovery of optimal quantum solutions. The presented framework incorporates key elements such as state representation, transition functions, and optimal substructure assumptions to guarantee efficiency and accuracy. This paper outlines the framework, its underlying principles, and potential applications within the broader field of quantum algorithm design.

DOI: 10.5281/zenodo.22471546

Related papers

Dynamic Programming for Probabilistic Circuit Optimization

Jincheng Zhang

Quantum circuit optimization remains a critical challenge in the development of quantum computing. Traditional dynamic programming (DP) methods, while effective for deterministic circuit design, fail to adequately address the inherent probabilistic nature of quantum operations. This paper proposes a novel approach that extends DP algorithms by explicitly incorporating probabilistic models representing uncertainties in quantum gate operations and qubit measurements. The core idea is to leverage Monte Carlo simulations to estimate expected costs and rewards within the DP framework. This allows for a more realistic and potentially efficient solution to the circuit optimization problem, considering the statistical fluctuations that are fundamental to quantum computing. We demonstrate the feasibility of this method conceptually, outlining the key components and algorithmic steps. Further research and implementation will be necessary to fully realize the potential of this approach.

Sep 7, 20260 citations

Dynamic Programming for Quantum Circuit Optimization with Error Mitigation

Jincheng Zhang

Quantum circuit optimization is a critical step in realizing the full potential of quantum computing. Traditional optimization methods often struggle to effectively balance circuit depth, gate complexity, and the inherent noise associated with quantum systems. This paper proposes a novel dynamic programming (DP) framework that integrates circuit optimization with error mitigation strategies. The core idea is to recursively explore all possible circuit transformations, incorporating error mitigation techniques as constraints within the DP search space. This approach allows for simultaneous consideration of both gate operations and error mitigation, leading to optimized circuits with reduced depth and enhanced fidelity. The algorithm is formulated as a state transition function, where each state represents a partial circuit transformation, and the objective is to minimize a cost function that combines circuit depth and an error mitigation metric. We demonstrate the feasibility and potential efficiency of this framework through a conceptual analysis and outline the key components of the implementation. Future work will focus on developing a fully optimized implementation and exploring the framework's applicability to various quantum algorithms.

Sep 3, 20260 citations

Dynamic Programming for Quantum Circuit Optimization with Error Modeling

Jincheng Zhang

Quantum circuit optimization is a critical step in realizing the full potential of quantum computing. However, the inherent noise and decoherence present in quantum systems introduce significant challenges to traditional optimization techniques. This paper proposes a novel approach that leverages dynamic programming (DP) to optimize quantum circuits while explicitly incorporating probabilistic error models. The core idea is to extend the DP table to represent not only the cost (gate count) of minimizing the circuit but also the estimated error probability associated with each sub-circuit. This allows for a more accurate assessment of the trade-off between circuit complexity and fidelity. The algorithm iteratively builds the DP table, considering different circuit decompositions and their corresponding error rates. The resulting optimized quantum circuit minimizes the overall expected error, providing a more robust solution compared to purely gate-count-based optimization. The methodology is presented with detailed formulas and mathematical notation, providing a comprehensive understanding of the approach. This work addresses a key limitation of existing optimization methods by integrating error modeling directly into the dynamic programming framework.

Sep 5, 20260 citations

Dynamic Programming for Quantum Circuit Optimization

Jincheng Zhang

Quantum circuit optimization is a critical challenge in the development and execution of quantum algorithms. The exponential growth in the complexity of quantum circuits necessitates efficient optimization techniques. This paper proposes a novel approach utilizing dynamic programming to systematically explore and minimize the resources (gate count and circuit depth) required for a given quantum circuit transformation. The core mechanism involves constructing a dynamic programming table to store the optimal solutions for subproblems, leveraging the overlapping subproblems inherent in the circuit transformation process. The algorithm systematically builds solutions from smaller circuit fragments, ultimately arriving at the globally optimal transformation. The potential scalability of this approach, combined with its ability to directly address the combinatorial nature of circuit optimization, offers a promising avenue for advancing quantum computing. This work provides a theoretical framework and outlines a detailed algorithm for dynamic programming-based quantum circuit optimization.

Aug 28, 20260 citations

Dynamic Programming with Quantum-Inspired Search Algorithms

Jincheng Zhang

This paper investigates the potential of accelerating dynamic programming (DP) algorithms by incorporating search strategies derived from quantum mechanics, specifically quantum tunneling and superposition. The core premise is that the inherent exploration capabilities of quantum phenomena can be simulated through quantum-inspired search algorithms, such as quantum annealing or evolutionary algorithms mimicking tunneling behavior, to efficiently navigate the solution space of DP problems. We propose a framework where a classical DP algorithm is augmented with a quantum-inspired search component. The aim is to leverage the strengths of both approaches – the precision and systematic nature of DP combined with the potentially faster exploration offered by quantum-inspired techniques. The effectiveness of this approach is evaluated through theoretical analysis and conceptual design, focusing on scenarios where traditional DP methods struggle with large state spaces or complex decision boundaries. This research contributes to a new paradigm in algorithm design, bridging the gap between classical and quantum computing by utilizing quantum-inspired methods to optimize classical algorithms. The core idea is to treat the DP problem as a tunneling event within a high-dimensional space, significantly reducing the time required to find optimal solutions.

Sep 1, 20260 citations

Dynamic Programming for Quantum Circuit Optimization with Uncertainty

Jincheng Zhang

Quantum circuit optimization is a crucial step in realizing the full potential of quantum computing. However, the inherent uncertainty in quantum gate fidelities and measurement outcomes presents a significant challenge. Traditional optimization methods often fail to adequately address this probabilistic nature. This paper proposes a novel dynamic programming approach for quantum circuit optimization that explicitly incorporates uncertainty. The algorithm constructs an optimal circuit path by minimizing the expected cost, which accounts for the potential error associated with each gate operation and measurement. This framework allows for a more accurate and robust optimization process, leading to circuits with reduced error and improved performance. The core claim is that dynamic programming can be effectively applied to quantum circuit optimization, acknowledging and utilizing the probabilistic elements. The key mechanism involves a structured, iterative process to evaluate and select the best circuit paths based on a quantified uncertainty model. This approach avoids the limitations of purely deterministic optimization techniques when dealing with quantum systems.

Sep 7, 20260 citations